Gravity - Revision history

Overthink: /* Intervals */ add this back

2026-03-29T00:31:00Z

Intervals: add this back

← Older revision		Revision as of 00:31, 29 March 2026
Line 21:		Line 21:

	== Intervals ==		== Intervals ==
	[[File:Gravity construction.png\|thumb\|right\|A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].\|960x320px]]		[[File:Gravity construction.png\|thumb\|right\|alt=Gravity construction.png\|A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].\|960x320px]]

	=== Interval chain ===		=== Interval chain ===

Overthink: formatting; link

2026-03-29T00:29:42Z

formatting; link

← Older revision		Revision as of 00:29, 29 March 2026
Line 20:		Line 20:
	For technical data, see [[Gravity family #Gravity]].		For technical data, see [[Gravity family #Gravity]].

	[[File:Gravity construction.png\|~~center~~\|~~alt=~~Gravity ~~construction~~.~~png~~\|960x320px]]		== Intervals ==
			[[File:Gravity construction.png\|thumb\|right\|A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].\|960x320px]]

	A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].

	~~== Intervals ==~~
	=== Interval chain ===		=== Interval chain ===
	In the following table, odd ~~harmonics~~ 1–15 are labeled in '''bold'''.		In the following table, [[odd harmonic]]s 1–15 are labeled in '''bold'''.

	{\| class="wikitable sortable center-1 right-2"		{\| class="wikitable sortable center-1 right-2"

FloraC: General cleanup

2026-03-27T14:19:41Z

General cleanup

← Older revision		Revision as of 14:19, 27 March 2026
Line 12:		Line 12:
	\| Odd limit 2 = 2.3.5.11 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 30		\| Odd limit 2 = 2.3.5.11 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 30
	}}		}}
	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the ~~interval~~ [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[~~129140163/128000000\|~~graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the [[6/1\|6th harmonic]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The [[5/1\|5th harmonic]] is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name follows.

	Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here ~~{{S\|9/S10}} =~~ [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and ~~S10/S11 =~~ [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[~~MOS~~ scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents ~~S9 =~~ [[81/80]], ~~S10 =~~ [[100/99]], and ~~S11 =~~ [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.		Gravity is most naturally seen as a [[2.3.5.11 subgroup\|2.3.5.11-subgroup]] temperament, sometimes known as '''larry'''. Here [[8019/8000]] ([[S-expression\|S9/S10]]) is tempered out, so that two intervals of 40/27 reach [[11/10]], and [[4000/3993]] ([[S-expression\|S10/S11]]) is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[mos scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}). In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.

	Strong extensions with prime 7 include [[gravid]] (58 & 65), 58 & 65d, [[marvo]] (65d & 72), and [[zarvo]] (65 & 72). However, the most notable extension of gravity is [[harry]] (58 & 72), which splits the octave in two and extends well to the 13- and [[17-limit]].		Strong extensions with prime 7 include [[gravid]] (58 & 65), 58 & 65d, [[marvo]] (65d & 72), and [[zarvo]] (65 & 72). However, the most notable extension of gravity is [[harry]] (58 & 72), which splits the octave in two and extends well to the 13- and [[17-limit]].

	~~{{tdlink\|~~Gravity family #Gravity}}		For technical data, see [[Gravity family #Gravity]].

			[[File:Gravity construction.png\|center\|alt=Gravity construction.png\|960x320px]]

	~~[[File:Gravity_construction.png\|alt=Gravity construction.png\|960x320px]]~~		A pictorial representation of the process of constructing the heptatonic mos of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting 6/1 in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].

	A pictorial representation of the process of constructing the heptatonic ~~MOS~~ of 2.3.5.11 gravity. Splitting 3/2 in two and splitting 4/3 in three are equivalent to splitting [[6/1]] in six, and Gravity[7] is equivalent to the scale obtained by octave-reducing [[6ed6]].

	== Intervals ==		== Intervals ==

	=== Interval chain ===		=== Interval chain ===
	In the following table, odd harmonics 1–15 are labeled in '''bold'''.		In the following table, odd harmonics 1–15 are labeled in '''bold'''.

	{\| class="wikitable sortable center-1 right-2"		{\| class="wikitable sortable center-1 right-2"
	! &#~~35;~~		! #
	! Cents*		! Cents*
	! class="unsortable" \| Approximate ratios		! class="unsortable" \| Approximate ratios
Line 131:		Line 129:
	\| '''15/8'''		\| '''15/8'''
	\|}		\|}
	<nowiki />* In 2.3.5.11-subgroup [[CTE tuning]]		<nowiki/>* In 2.3.5.11-subgroup [[CTE tuning]]

	=== As a detempering of 7et ===		=== As a detempering of 7et ===
	{{~~todo\|add detempering info~~\|inline=1}}		{{Todo\|inline=1\|complete section\|comment = Add detempering info.}}

	== Tunings ==		== Tunings ==
Line 141:		Line 139:
	=== Tuning spectrum ===		=== Tuning spectrum ===
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	! ~~EDO~~<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]*		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]*
	! Generator (¢)		! Generator (¢)
Line 184:		Line 182:
	\| [[11/8]]		\| [[11/8]]
	\| 516.7545		\| 516.7545
	\| (2.3.5.11) 11-odd-limit minimax tuning		\| 2.3.5.11 11-odd-limit minimax tuning
	\|-		\|-
	\|		\|
	\| [[5/3]]		\| [[5/3]]
	\| 516.7599		\| 516.7599
	\| 2/11-comma, (2.3.5.11) 15-odd-limit minimax tuning		\| 2/11-comma, 2.3.5.11 15-odd-limit minimax tuning
	\|-		\|-
	\| [[137edo\|59\137]]		\| [[137edo\|59\137]]
Line 264:		Line 262:
	\|		\|
	\| '''520.0000'''		\| '''520.0000'''
	\| 30bccee val, '''upper bound of (2.3.5.11) 11- and 15-odd-limit diamond monotone'''		\| 30bccee val, '''upper bound of 2.3.5.11 11- and 15-odd-limit diamond monotone'''
	\|-		\|-
	\| '''[[23edo\|10\23]]'''		\| '''[[23edo\|10\23]]'''
	\|		\|
	\| '''521.7391'''		\| '''521.7391'''
	\| 23bcccee val, '''upper bound of (2.3.5) 5- and 9-odd-limit diamond monotone'''		\| 23bcccee val, '''upper bound of 2.3.5 5- and 9-odd-limit diamond monotone'''
	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

FloraC: Cleanup on infobox

2026-02-09T09:15:28Z

Cleanup on infobox

← Older revision		Revision as of 09:15, 9 February 2026
Line 2:		Line 2:
	\| Title = Gravity; Larry		\| Title = Gravity; Larry
	\| Subgroups = 2.3.5, 2.3.5.11		\| Subgroups = 2.3.5, 2.3.5.11
	\| Comma basis = [[129140163/128000000]] (2.3.5); <br> [[243/242]], [[4000/3993]] (2.3.5.11)		\| Comma basis = [[129140163/128000000]] (2.3.5); <br>[[243/242]], [[4000/3993]] (2.3.5.11)
	\| Edo join 1 = 7 \| Edo join 2 = 58		\| Edo join 1 = 7 \| Edo join 2 = 58
	~~\| Generator = 27/20 \| Generator tuning = 516.8 \| Optimization method = POTE~~
	~~\| MOS scales = [[2L 5s]], [[7L 2s]], [[7L 9s]], ..., [[7L 51s]]~~
	\| Mapping = 1; 6 17 15		\| Mapping = 1; 6 17 15
			\| Generators = 27/20 \| Generators tuning = 516.8 \| Optimization method = CWE
			\| MOS scales = [[2L 5s]], [[7L 2s]], [[7L 9s]], …, [[7L 51s]]
	\| Pergen = (P8, P19/6)		\| Pergen = (P8, P19/6)
	\| Color name = Lala-tribiguti		\| Color name = Lala-tribiguti
	\| Odd limit 1 = 5 \| Mistuning 1 = 0.90 \| Complexity 1 = 23		\| Odd limit 1 = 5 \| Mistuning 1 = 0.90 \| Complexity 1 = 23
	\| Odd limit 2 = (2.3.5.11) 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 30		\| Odd limit 2 = 2.3.5.11 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 30
	}}		}}

	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.

Overthink: made scale sizes more reasonable

2025-11-16T18:48:20Z

made scale sizes more reasonable

← Older revision		Revision as of 18:48, 16 November 2025
Line 9:		Line 9:
	\| Pergen = (P8, P19/6)		\| Pergen = (P8, P19/6)
	\| Color name = Lala-tribiguti		\| Color name = Lala-tribiguti
	\| Odd limit 1 = 5 \| Mistuning 1 = 0.90 \| Complexity 1 = 37		\| Odd limit 1 = 5 \| Mistuning 1 = 0.90 \| Complexity 1 = 23
	\| Odd limit 2 = (2.3.5.11) 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 51		\| Odd limit 2 = (2.3.5.11) 15 \| Mistuning 2 = 1.48 \| Complexity 2 = 30
	}}		}}

Overthink: capitalized larry in infobox

2025-11-16T18:47:23Z

capitalized larry in infobox

← Older revision		Revision as of 18:47, 16 November 2025
Line 1:		Line 1:
	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Gravity; ~~larry~~		\| Title = Gravity; Larry
	\| Subgroups = 2.3.5, 2.3.5.11		\| Subgroups = 2.3.5, 2.3.5.11
	\| Comma basis = [[129140163/128000000]] (2.3.5); <br> [[243/242]], [[4000/3993]] (2.3.5.11)		\| Comma basis = [[129140163/128000000]] (2.3.5); <br> [[243/242]], [[4000/3993]] (2.3.5.11)

Squib at 19:53, 10 September 2025

2025-09-10T19:53:18Z

← Older revision		Revision as of 19:53, 10 September 2025
Line 13:		Line 13:
	}}		}}

	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}); The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.

	Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.		Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.

Squib at 19:50, 10 September 2025

2025-09-10T19:50:46Z

← Older revision		Revision as of 19:50, 10 September 2025
Line 13:		Line 13:
	}}		}}

	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), and thereby ~~characterized by the vanishing of~~ the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}); ~~the 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total.~~ The complement of the acute fourth is the grave fifth, [[40/27]], whence the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), dividing the fifth in two and the fourth in three. The 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total, thereby tempering out the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}); The complement of the acute fourth generator is the grave fifth, [[40/27]], whence the temperament's name.

	Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.		Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.

Lériendil at 01:51, 22 June 2025

2025-06-22T01:51:55Z

← Older revision		Revision as of 01:51, 22 June 2025
Line 13:		Line 13:
	}}		}}

	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), and thereby characterized by the vanishing of the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }})~~. The fifth~~ harmonic is found at three fifths up and one generator down, or 17 generators in total. The complement of the acute fourth is the grave fifth, [[40/27]], whence the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), and thereby characterized by the vanishing of the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}); the 5th harmonic is found at three perfect fifths up and one generator down, or 17 generators in total. The complement of the acute fourth is the grave fifth, [[40/27]], whence the temperament's name.

	Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.		Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.

Lériendil at 01:50, 22 June 2025

2025-06-22T01:50:53Z

← Older revision		Revision as of 01:50, 22 June 2025
Line 13:		Line 13:
	}}		}}

	'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]], and thereby characterized by the vanishing of the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The complement of the acute fourth is the grave fifth, [[40/27]], ~~hence~~ the temperament's name.		'''Gravity''' is a [[rank-2 temperament\|rank-2]] [[regular temperament\|temperament]] and parent of the [[gravity family]], [[generator\|generated]] by a [[27/20\|classical acute fourth (27/20)]], six of which stacked reach the interval [[6/1]] (which octave reduces to the perfect fifth, [[3/2]]), and thereby characterized by the vanishing of the [[129140163/128000000\|graviton]] ([[ratio]]: 129140163/128000000, {{monzo\|legend=1\| -13 17 -6 }}). The fifth harmonic is found at three fifths up and one generator down, or 17 generators in total. The complement of the acute fourth is the grave fifth, [[40/27]], whence the temperament's name.

	Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.		Gravity is most naturally seen as a [[2.3.5.11 subgroup]] temperament, sometimes known as '''larry'''. Here {{S\|9/S10}} = [[8019/8000]] is tempered out, so that two intervals of 40/27 reach [[11/10]], and S10/S11 = [[4000/3993]] is tempered out, so that three intervals of 11/10 reach 4/3. These equivalences also imply that [[243/242]] is tempered out; three 27/20 fourths reach [[11/9]], which is thus equated to [[27/22]] and acts as an exact neutral third. Gravity's generator lies close to the fifth of [[7edo]], implying that the [[MOS scale]]s of gravity [[cluster temperament\|cluster]] heavily around 7edo, and in this interpretation the comma reached after 7 generators simultaneously represents S9 = [[81/80]], S10 = [[100/99]], and S11 = [[121/120]]. In fact, gravity can be completely defined by making this equivalence between three adjacent square superparticulars, being the most accurate of the 5 temperaments definable in such a way.